Weighted Morrey Spaces Research Articles

Weighted Estimates for Maximal Operators, Riesz Potential Operators and Commutators on p-Adic Lebesgue and Morrey Spaces

In this paper, we establish the boundedness of p-adic Hardy-Littlewood maximal operators and p-adic Riesz potential operators on the weighted Lebsegue and Morrey spaces. Moreover, the boundedness for the commutators of p-adic Riesz potential operators on the weighted Morrey spaces with symbols in central BMO space is also given.

Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces

In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear operators including many interesting in harmonic analysis and its commutators on the weighted Morrey spaces. Finally, as an application, the boundedness of strongly singular integral operators and commutators with symbols in BMO space are also given.

Weighted complete continuity for the commutator of Marcinkiewicz integral

Let $\Omega$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\mathcal{M}_{\Omega}$ be the higher-dimensional Marcinkiewicz integral associated with $\Omega$. In this paper, the author considers the complete continuity on weighted $L^p(\mathbb{R}^n)$ spaces with $A_p(\mathbb{R}^n)$ weights, weighted Morrey spaces with $A_p(\mathbb{R}^n)$ weights, for the commutator generated by ${\rm CMO}(\mathbb{R}^n)$ functions and $\mathcal{M}_{\Omega}$ when $\Omega$ satisfies certain size conditions.

Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group

In this paper, we study the high-dimensional Hausdorff operators, defined via a general linear mapping $A$, and their commutators on the weighted Morrey spaces in the setting of the Heisenberg group. Particularly, under some assumption on the mapping $A$, we establish their sharp boundedness on the power weighted Morrey spaces.

On the Behaviors of Rough Fractional Type Sublinear Operators on Vanishing Generalized Weighted Morrey Spaces

The aim of this paper is to get the boundedness of rough sublinear operators generated by fractional integral operators on vanishing generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. Also, rough fractional integral operator and a related rough fractional maximal operator which satisfy the conditions of our main result can be considered as some examples.

The Dirichlet problem in a class of generalized weighted Morrey spaces

We show continuity in generalized weighted Morrey spaces Mp,'(w) of sub-linear integral operators generated by some classical integral operators and commutators. The obtained esti- mates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operators with dis- continuous data.

Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent

Let $\Omega \subset \mathbb{R}^n$ be an unbounded open set. We consider the generalized weighted Morrey spaces $\mathcal{M}^{p(\cdot),\varphi}_{\omega}(\Omega)$ and the vanishing generalized weighted Morrey spaces $V\mathcal{M}^{p(\cdot),\varphi}_{\omega}(\Omega)$ with variable exponent $p(x)$ and a general function $\varphi(x,r)$ defining the Morrey-type norm. The main result of this paper are the boundedness of Riesz potential and its commutators on the spaces $\mathcal{M}^{p(\cdot),\varphi}_{\omega}(\Omega)$ and $V\mathcal{M}^{p(\cdot),\varphi}_{\omega}(\Omega)$. This result generalizes several existing results for Riesz potential and its commutators on Morrey type spaces. Especially, it gives a unified result for generalized Morrey spaces and variable Morrey spaces which currently gained a lot of attentions from researchers in theory of function spaces.

Boundedness of Toeplitz operators related to singular integral operators

We establish that Toeplitz-type operators related to singular integral operators with variable Calderón– Zygmund kernels are bounded on weighted Morrey spaces. To do this, we prove weighted inequalities for the sharp maximal functions of such operators.

On the behavior of a class of fractional type rough higher order commutators on generalized weighted Morrey spaces

On the behavior of a class of fractional type rough higher order commutators on generalized weighted Morrey spaces

English

We first introduce new weighted Morrey spaces related to certain non-negative potentials satisfying the reverse Holder inequality. Then we establish the weighted strong-type and weak-type estimates for the Riesz transforms and fractional integrals associated to Schrodinger operators. As an application, we prove the Calderon-Zygmund estimates for solutions to Schrodinger equation on these new spaces. Our results cover a number of known results.

Pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spaces

In this paper, a local good $$\lambda $$ inequality for a class of new weight functions which include Muckenhoupt weight functions is established. Applying the local good $$\lambda $$ inequality and new sharp maximal functions, the authors give a characterization of weighted Morrey spaces. Furthermore, it is proved that the boundedness of pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spaces.

Maximal and singular integral operators and their commutators on generalized weighted Morrey spaces with variable exponent

Maximal and singular integral operators and their commutators on generalized weighted Morrey spaces with variable exponent

Maximal and singular integral operators and their commutators on generalized weighted Morrey spaces with variable exponent

Maximal and singular integral operators and their commutators on generalized weighted Morrey spaces with variable exponent

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces

Extension and Boundedness of Operators on Morrey Spaces from Extrapolation Techniques and Embeddings

We prove that operators satisfying the hypotheses of the extrapolation theorem for Muckenhoupt weights are bounded on weighted Morrey spaces. As a consequence, we obtain at once a number of results that have been proved individually for many operators. On the other hand, our theorems provide a variety of new results even for the unweighted case because we do not use any representation formula or pointwise bound of the operator as was assumed by previous authors. To extend the operators to Morrey spaces we show different (continuous) embeddings of (weighted) Morrey spaces into appropriate Muckenhoupt $$A_1$$ weighted $$L_p$$ spaces, which enable us to define the operators on the considered Morrey spaces by restriction. In this way, we can avoid the delicate problem of the definition of the operator, often ignored by the authors. In dealing with the extension problem through the embeddings (instead of using duality), one is neither restricted in the parameter range of the p’s (in particular $$p=1$$ is admissible and applies to weak-type inequalities) nor the operator has to be linear. Another remarkable consequence of our results is that vector-valued inequalities in Morrey spaces are automatically deduced. On the other hand, we also obtain $$A_\infty $$ -weighted inequalities with Morrey quasinorms.

Another characterizations of Muckenhoupt Ap class

This manuscript addresses Muckenhoupt Ap weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces Lp(ω) to weighted Morrey spaces Mqp(ω) for 1 <q <p < ∞. As a corollary, if M is (weak) bounded on Mqp(ω), then ω ∈ Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tɛ on weighted Morrey spaces. Finally, we show that ω ∈ Ap if and only if ω ∈BMOp′(ω) for 1 ≤ p < ∞ and 1/p+1/p′=1.

Boundedness of Parametrized Littlewood-Paley Operators with Variable Kernels on weighted Morrey Spaces

In this paper,we establish the boundedness of parameterized area integral \(\mu_{\Omega,S}^{\rho}\) and the Littlewood-Paley \(g_{\lambda}^{\ast}\) function \(\mu_{\Omega,\lambda}^{\ast,\rho}\) with variable kernel on weighted Morrey space \(L^{p,k}(\omega)\).

Weighted Morrey spaces on non-homogeneous metric measure spaces

Let (X,d,μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. In this setting, the authors introduce the weighted Morrey space and the weighted weak Morrey space, and show several properties of these spaces. As applications, some weighted weak type estimates for the Hardy–Littlewood maximal operator and the Calderón–Zygmund type operator are established.

Some Estimates for Generalized Commutators of Rough Fractional Maximal and Integral Operators on Generalized Weighted Morrey Spaces

AbstractIn this paper, we establish BMO estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, respectively.

The singular integral operator and its commutator on weighted Morrey spaces

In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the $$A_q$$ -theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.